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Radiomics can quantify the properties of regions of interest in medical image data. Classically, they account for pre-defined statistics of shape, texture, and other low-level image features. Alternatively, deep learning-based representations are derived from supervised learning but require expensive annotations and often suffer from overfitting and data imbalance issues. In this work, we address the challenge of learning the representation of a 3D medical image for an effective quantification under data imbalance. We propose a self-supervised representation learning framework to learn high-level features of 3D volumes as a complement to existing radiomics features. Specifically, we demonstrate how to learn image representations in a self-supervised fashion using a 3D Siamese network. More importantly, we deal with data imbalance by exploiting two unsupervised strategies: a) sample re-weighting, and b) balancing the composition of training batches. When combining the learned self-supervised feature with traditional radiomics, we show significant improvement in brain tumor classification and lung cancer staging tasks covering MRI and CT imaging modalities. Codes are available in https://github.com/hongweilibran/imbalanced-SSL.